Journal article Open Access

On Completeness in Metric Spaces and Fixed Point Theorems

Valentin Gregori; Juan José Miñana; Bernardino Roig; Almanzor Sapena


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    <subfield code="a">This is a preprint of the publication available from https://link.springer.com/article/10.1007/s00025-018-0896-4. This work is also supported by project PGC2018-095709-B-C21 (MCIU/AEI/FEDER, UE), and PROCOE/4/2017 (Govern Balear, 50% P.O. FEDER 2014-2020 Illes Balears).</subfield>
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    <subfield code="a">On Completeness in Metric Spaces and Fixed Point Theorems</subfield>
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    <subfield code="a">&lt;p&gt;Complete ultrametric spaces constitute a particular class of the so called, recently, G-complete metric spaces. In this paper we characterize a more general class called weak G-complete metric spaces, by means of nested sequences of closed sets. Then, we also state a general fixed point theorem for a self-mapping of a weak G-complete metric space. As a corollary, every asymptotically regular self-mapping of a weak G-Complete metric space has a fixed point.&lt;/p&gt;</subfield>
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